The Veneto has so much to offer with many small towns including the delightful Asolo, one of my late husband‘s favourite places in Italy.
Realistically though for train travel I agree with others Vicenza, and Padua are very rewarding places to visit.
The Teatro Olimpico in Vicenza is one of Palladio‘s marvels in my opinion and of course, La Rotonda a World Heritage site. You’d probably need a taxi from Vicenza however. Padua is a fabulous place for a day or longer visit but make sure you take refreshments at Gran Cafe Pedrocchi probably included in Rossi writes as above.
We visited many of the villas in the Veneto and were not disappointed.
One of our favourites;
https://www.valsanzibiogiardino.com/
I‘m not sure if you can still sail up the Brenta to view some as you glide by, alternatively you could get to Padua that way from Venice or take a whole day visiting villas by boat.
Agree with others, Treviso, Bassano, great places to visit.
A month in Venice/ the Veneto sounds utterly blissful to me. Getting away from the hoards in Venice to places fairly close by on day trips makes for a great contrast. Perfect Slow Travel !
Lucky you !